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Last updated:

September 23, 2023

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Description

Advanced Matrix Theory and Linear Algebra for Engineers. Instructor: Prof. Vittal Rao, Centre for Electronics Design and Technology, IISc Bangalore.

Introduction to systems of linear equations, Vector spaces, Solutions of linear systems, Important subspaces associated with a matrix, Orthogonality, Eigenvalues and eigenvectors, Diagonalizable matrices, Hermitian and symmetric matrices, General matrices. (from nptel.ac.in)

Course Curriculum

    • Lecture 01 – Prologue Part 1: Systems of Linear Equations, Matrix Notation Unlimited
    • Lecture 02 – Prologue Part 2: Diagonalization of a Square Matrix Unlimited
    • Lecture 03 – Prologue Part 3: Homogeneous Systems, Elementary Row Operations Unlimited
    • Lecture 04 – Linear Systems 1: Elementary Row Operations (EROs) Unlimited
    • Lecture 05 – Linear Systems 2: Row Reduced Echelon Form, The Reduction Process Unlimited
    • Lecture 06 – Linear Systems 3: The Reduction Process, Solution using EROs Unlimited
    • Lecture 07 – Linear Systems 4: Solution using EROs: Non-homogeneous Systems Unlimited
    • Lecture 08 – Vector Spaces Part 1 Unlimited
    • Lecture 09 – Vector Spaces Part 2 Unlimited
    • Lecture 10 – Linear Combination, Linear Independence and Dependence Unlimited
    • Lecture 11 – Linear Independence and Dependence, Subspaces Unlimited
    • Lecture 12 – Subspace Spanned by a Finite Set of Vectors, The Basic Subspaces … Unlimited
    • Lecture 13 – Subspace Spanned by an Infinite Set of Vectors, Linear Independence of … Unlimited
    • Lecture 14 – Basis, Basis as a Maximal Linearly Independent Set Unlimited
    • Lecture 15 – Finite Dimensional Vector Spaces Unlimited
    • Lecture 16 – Extension of a Linearly Independent Set to a Basis, Ordered Basis Unlimited
    • Lecture 17 – Relation between Representation in Two Bases, Linear Transformations Unlimited
    • Lecture 18 – Examples of Linear Transformations Unlimited
    • Lecture 19 – Null Space and Range of a Linear Transformation Unlimited
    • Lecture 20 – Rank Nullity Theorem, One-One Linear Transformation Unlimited
    • Lecture 21 – One-One Linear Transformation, Onto Linear Transformations, Isomorphisms Unlimited
    • Lecture 22 – Inner Product and Orthogonality Unlimited
    • Lecture 23 – Orthonormal Sets, Orthonormal Basis and Fourier Expansion Unlimited
    • Lecture 24 – Fourier Expansion, Gram-Schmidt Orthonormalization, Orthogonal Complements Unlimited
    • Lecture 25 – Orthogonal Complements, Decomposition of a Vector, Pythagoras Theorem Unlimited
    • Lecture 26 – Orthogonal Complements in the context of Subspaces Associated with a Matrix Unlimited
    • Lecture 27 – Best Approximation Unlimited
    • iagonalization Lecture 28 – Diagonalization, Eigenvalues and Eigenvectors Unlimited
    • Lecture 29 – Eigenvalues and Eigenvectors, Characteristic Polynomial Unlimited
    • Lecture 30 – Algebraic Multiplicity, Eigenvectors, Eigenspaces and Geometric Multiplicity Unlimited
    • Lecture 31 – Criterion for Diagonalization Unlimited
    • Lecture 32 – Hermitian and Symmetric Matrices, Unitary Matrix Unlimited
    • Lecture 33 – Unitary and Orthogonal Matrices, Eigen Properties of Hermitian Matrices, … Unlimited
    • Lecture 34 – Spectral Decomposition Unlimited
    • Lecture 35 – Positive and Negative Definite and Semidefinite Matrices Unlimited
    • Lecture 36 – Singular Value Decomposition (SVD) Part 1 Unlimited
    • Lecture 37 – Singular Value Decomposition (SVD) Part 2 Unlimited
    • Lecture 38 – Back to Linear Systems Part 1 Unlimited
    • Lecture 39 – Back to Linear Systems Part 2 Unlimited

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